Kimura, Hironobu; Koitabashi, Toshiyuki Normalizer of maximal abelian subgroups of \(\mathrm{GL}(n)\) and general hypergeometric functions. (English) Zbl 0848.33009 Kumamoto J. Math. 9, 13-43 (1996). The generalized confluent hypergeometric systems on the Grassmannian have been formulated in the earlier papers of I. M. Gel’fand, V. S. Retakh, and V. V. Serganova [Generalized Airy functions, Schubert cells, and Jordan groups, Sov. Math., Dokl. 37, No. 1, 8–12 (1988); translation from Dokl. Akad. Nauk SSSR 298, No. 1, 17–21 (1988; Zbl 0699.33012)] and H. Kimura, Y. Haraoka, and K. Takano [Generalized confluent hypergeometric functions, Proc. Jap. Acad., Ser. A 68, 290–295 (1992; Zbl 0773.33004)]. The paper clarifies the symmetry of the confluent hypergeometric systems in terms of the action of the normalizer of maximal abelian subgroups of \(\mathrm{GL}(n)\). The symmetry particularly reveals several transformation formulas for the classical confluent hypergeometric functions. Reviewer: T.Sasaki (Kobe) Cited in 3 ReviewsCited in 7 Documents MSC: 33C80 Connections of hypergeometric functions with groups and algebras, and related topics 33C70 Other hypergeometric functions and integrals in several variables 33C65 Appell, Horn and Lauricella functions Keywords:confluent hypergeomemetric function; symmetry of confluent hypergeometric systems PDF BibTeX XML Cite \textit{H. Kimura} and \textit{T. Koitabashi}, Kumamoto J. Math. 9, 13--43 (1996; Zbl 0848.33009)